
Authors:
Mladen VUKOVIC
Title:HennessyMilner Theorem for Interpretability Logic
Pages:195201
File:bibtex
Abstract ( + )
Interpretability logic is a modal description of the interpretability predicate. The modal system IL is an extension of the provability logic GL GoedelLoeb. We define bisimulations between generalized Veltman models, i.e. IL_{set}models. Then we consider some operations between models and prove that the operations are a special case of bisimulation. At the end we prove HennessyMilner theorem for IL_{set}models.

Authors:
L. DESCALCO and Manuel A. MARTINS
Title:On the Injectivity of the Leibniz Operator
Pages:203211
File:bibtex
Abstract ( + )
The class weakly algebrizable logics is defined as the class of logics having monotonic and injective Leibniz operator. We show that "monotonicity" cannot be discarded on this definition, by presenting an example of a system with injective and non monotonic Leibniz operator.

Authors:
Norihiro KAMIDE
Title:A Cutfree System for 16Valued Reasoning
Pages:213225
File:bibtex
Abstract ( + )
A sequent calculus L16 for a 16valued logic is introduced as an extension of a sequent calculus for Belnap's 4valued logic. The cutelimination theorem for L16 is proved using an embedding from L16 into a sequent calculus for the implicationfree positive classical logic. It is shown that Shramko and Wansing's 16valued logic of truth order, which is closely related to trilattices, is a subsystem of L16.

Authors:
Boguslaw WOLNIEWICZ
Title:On a Minimality Condition
Pages:227228
File:bibtex
Abstract ( + )
[Abstract]

Authors:
Krystyna MRUCZEKNASIENIEWSKA and Marek NASIENIEWSKI
Title:Syntactical and Semantical Characterization of a Class of Paraconsistent Logics
Pages:229248
File:bibtex
Abstract ( + )
The paper presents a modal formulation of some propositional logics. The idea was used by JeanYves Beziau who formulated logic Z with the help of the logic S5. The formulation of the logic Z uses a transformation from the set of classical propositional formulae to the set of modal propositional formulae. This formulation is in a sense similar to Jaskowki's formulation of logic D2. The idea also refers to works by Segerberg, Rasiowa and Vakarelov. The main results of the paper are Lemma 16, and Theorem 1 presenting a class of propositional logics obtained with the help of Beziau's transformation, however, this transformation is applied to other modal logics. As Remark 2 and Theorem 2 prove, a lot of presented propositional logics are paraconsistent.